Manuals/calci/PENTADIAGONAL

MATRIX("PENTADIAGONAL",order)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle order} is the size of the Pentadiagonal matrix.

Description

• This function gives the pentadiagonal matrix of order 3.
• A pentadiagonal matrix is a matrix that is nearly diagonal.
• So it is a matrix in which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it.
• The form of pentadiagonal matrix is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=\begin{pmatrix} c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\ b_1 & c_2 & d_2 & e_2 & \ddots & & \vdots \\ a_1 & b_2 & \cdots & \ddots & \ddots & \ddots & \vdots \\ 0 & a_2 & \cdots & \ddots & \ddots & e_{n-3} & 0 \\ \vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\ \vdots & & \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\ 0 & \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n \end{pmatrix}} .

• When n is the size of the matrix, a pentadiagonal matrix has atmost 5n-6 nonzero entries.
• Here MATIRX("pentadiagonal") is showing the penta diagonal matrix of order 3 with the integer numbers.
• Also in Calci users can get a deimal values with positive and negative numbers.
• The syntax is to get the decimal penta diagonal matrix is MATRIX("pentadiagonal:negative") and MATRIX(pentadiagonal:positive")